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    <ul class="crumbs"><li><a href="../index.html">Home</a></li><li><a href="../services.html">Services</a></li><li><a href="index.html">calculus</a></li><li><a href="index.html#3">Chapter 3: Binary Predicates</a></li><li><b>The Equality Relation</b></li></ul></div>
<p class="purpose">To define that prince among predicates, the equality relation; and also its less noble sidekick, the "has" relation.</p>

<ul class="toc"><li><a href="3-ter.html#SP2">&#167;2. Family</a></li><li><a href="3-ter.html#SP3">&#167;3. Initial stock</a></li><li><a href="3-ter.html#SP4">&#167;4. Problem message text</a></li></ul><hr class="tocbar">

<p class="commentary firstcommentary"><a id="SP1" class="paragraph-anchor"></a><b>&#167;1. </b>Equality is the only relation in its family; but in Inform, there will be other
relations besides "has" in the spatial family.
</p>

<pre class="displayed-code all-displayed-code code-font">
<span class="reserved-syntax">bp_family</span><span class="plain-syntax"> *</span><span class="identifier-syntax">equality_bp_family</span><span class="plain-syntax"> = </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>
<span class="reserved-syntax">bp_family</span><span class="plain-syntax"> *</span><span class="identifier-syntax">spatial_bp_family</span><span class="plain-syntax"> = </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>
<span class="reserved-syntax">bp_family</span><span class="plain-syntax"> *</span><span class="identifier-syntax">dialogue_bp_family</span><span class="plain-syntax"> = </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>
<span class="reserved-syntax">bp_family</span><span class="plain-syntax"> *</span><span class="identifier-syntax">empty_bp_family</span><span class="plain-syntax"> = </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>

<span class="reserved-syntax">binary_predicate</span><span class="plain-syntax"> *</span><span class="identifier-syntax">R_equality</span><span class="plain-syntax"> = </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>
<span class="reserved-syntax">binary_predicate</span><span class="plain-syntax"> *</span><span class="identifier-syntax">a_has_b_predicate</span><span class="plain-syntax"> = </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>
<span class="reserved-syntax">binary_predicate</span><span class="plain-syntax"> *</span><span class="identifier-syntax">R_empty</span><span class="plain-syntax"> = </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>
</pre>
<p class="commentary firstcommentary"><a id="SP2" class="paragraph-anchor"></a><b>&#167;2. Family.</b>This is a minimal representation only, for when the calculus module is used
in a non-Inform context: whereas Inform adds other methods to the equality
family to handle its typechecking in <a href="../assertions-module/8-terr.html" class="internal">The Equality Relation Revisited (in assertions)</a>.
</p>

<pre class="displayed-code all-displayed-code code-font">
<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Calculus::Equality::start</span><button class="popup" onclick="togglePopup('usagePopup1')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup1">Usage of <span class="code-font"><span class="function-syntax">Calculus::Equality::start</span></span>:<br/>Calculus Module - <a href="1-cm.html#SP3">&#167;3</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">void</span><span class="plain-syntax">) {</span>
<span class="plain-syntax">    </span><span class="identifier-syntax">equality_bp_family</span><span class="plain-syntax"> = </span><a href="3-bpf.html#SP1" class="function-link"><span class="function-syntax">BinaryPredicateFamilies::new</span></a><span class="plain-syntax">();</span>
<span class="plain-syntax">    </span><span class="identifier-syntax">METHOD_ADD</span><span class="plain-syntax">(</span><span class="identifier-syntax">equality_bp_family</span><span class="plain-syntax">, </span><span class="constant-syntax">STOCK_BPF_MTID</span><span class="plain-syntax">,</span>
<span class="plain-syntax">        </span><a href="3-ter.html#SP3" class="function-link"><span class="function-syntax">Calculus::Equality::stock</span></a><span class="plain-syntax">);</span>
<span class="plain-syntax">    </span><span class="identifier-syntax">METHOD_ADD</span><span class="plain-syntax">(</span><span class="identifier-syntax">equality_bp_family</span><span class="plain-syntax">, </span><span class="constant-syntax">DESCRIBE_FOR_PROBLEMS_BPF_MTID</span><span class="plain-syntax">,</span>
<span class="plain-syntax">        </span><a href="3-ter.html#SP4" class="function-link"><span class="function-syntax">Calculus::Equality::describe_for_problems</span></a><span class="plain-syntax">);</span>
<span class="plain-syntax">    </span><span class="identifier-syntax">METHOD_ADD</span><span class="plain-syntax">(</span><span class="identifier-syntax">equality_bp_family</span><span class="plain-syntax">, </span><span class="constant-syntax">DESCRIBE_FOR_INDEX_BPF_MTID</span><span class="plain-syntax">,</span>
<span class="plain-syntax">        </span><a href="3-ter.html#SP4" class="function-link"><span class="function-syntax">Calculus::Equality::describe_for_index</span></a><span class="plain-syntax">);</span>

<span class="plain-syntax">    </span><span class="identifier-syntax">spatial_bp_family</span><span class="plain-syntax"> = </span><a href="3-bpf.html#SP1" class="function-link"><span class="function-syntax">BinaryPredicateFamilies::new</span></a><span class="plain-syntax">();</span>
<span class="plain-syntax">    #</span><span class="identifier-syntax">ifndef</span><span class="plain-syntax"> </span><span class="identifier-syntax">IF_MODULE</span>
<span class="plain-syntax">    </span><span class="identifier-syntax">METHOD_ADD</span><span class="plain-syntax">(</span><span class="identifier-syntax">spatial_bp_family</span><span class="plain-syntax">, </span><span class="constant-syntax">STOCK_BPF_MTID</span><span class="plain-syntax">,</span>
<span class="plain-syntax">        </span><a href="3-ter.html#SP3" class="function-link"><span class="function-syntax">Calculus::Equality::stock_spatial</span></a><span class="plain-syntax">);</span>
<span class="plain-syntax">    #</span><span class="identifier-syntax">endif</span>

<span class="plain-syntax">    </span><span class="identifier-syntax">dialogue_bp_family</span><span class="plain-syntax"> = </span><a href="3-bpf.html#SP1" class="function-link"><span class="function-syntax">BinaryPredicateFamilies::new</span></a><span class="plain-syntax">();</span>

<span class="plain-syntax">    </span><span class="identifier-syntax">empty_bp_family</span><span class="plain-syntax"> = </span><a href="3-bpf.html#SP1" class="function-link"><span class="function-syntax">BinaryPredicateFamilies::new</span></a><span class="plain-syntax">();</span>
<span class="plain-syntax">    </span><span class="identifier-syntax">METHOD_ADD</span><span class="plain-syntax">(</span><span class="identifier-syntax">empty_bp_family</span><span class="plain-syntax">, </span><span class="constant-syntax">STOCK_BPF_MTID</span><span class="plain-syntax">,</span>
<span class="plain-syntax">        </span><a href="3-ter.html#SP3" class="function-link"><span class="function-syntax">Calculus::Equality::stock_empty</span></a><span class="plain-syntax">);</span>
<span class="plain-syntax">    </span><span class="identifier-syntax">METHOD_ADD</span><span class="plain-syntax">(</span><span class="identifier-syntax">empty_bp_family</span><span class="plain-syntax">, </span><span class="constant-syntax">DESCRIBE_FOR_PROBLEMS_BPF_MTID</span><span class="plain-syntax">,</span>
<span class="plain-syntax">        </span><a href="3-ter.html#SP4" class="function-link"><span class="function-syntax">Calculus::Equality::describe_empty_for_problems</span></a><span class="plain-syntax">);</span>
<span class="plain-syntax">    </span><span class="identifier-syntax">METHOD_ADD</span><span class="plain-syntax">(</span><span class="identifier-syntax">empty_bp_family</span><span class="plain-syntax">, </span><span class="constant-syntax">DESCRIBE_FOR_INDEX_BPF_MTID</span><span class="plain-syntax">,</span>
<span class="plain-syntax">        </span><a href="3-ter.html#SP4" class="function-link"><span class="function-syntax">Calculus::Equality::describe_empty_for_index</span></a><span class="plain-syntax">);</span>
<span class="plain-syntax">}</span>
</pre>
<p class="commentary firstcommentary"><a id="SP3" class="paragraph-anchor"></a><b>&#167;3. Initial stock.</b>Note the unique one-off way in which equality is made.
</p>

<pre class="displayed-code all-displayed-code code-font">
<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Calculus::Equality::stock</span><button class="popup" onclick="togglePopup('usagePopup2')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup2">Usage of <span class="code-font"><span class="function-syntax">Calculus::Equality::stock</span></span>:<br/><a href="3-ter.html#SP2">&#167;2</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">bp_family</span><span class="plain-syntax"> *</span><span class="identifier-syntax">self</span><span class="plain-syntax">, </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">n</span><span class="plain-syntax">) {</span>
<span class="plain-syntax">    </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">n</span><span class="plain-syntax"> == </span><span class="constant-syntax">1</span><span class="plain-syntax">) {</span>
<span class="plain-syntax">        </span><span class="identifier-syntax">R_equality</span><span class="plain-syntax"> = </span><a href="3-bp.html#SP9" class="function-link"><span class="function-syntax">BinaryPredicates::make_equality</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">equality_bp_family</span><span class="plain-syntax">,</span>
<span class="plain-syntax">            </span><span class="identifier-syntax">PreformUtilities::wording</span><span class="plain-syntax">(</span><span class="function-syntax">&lt;relation-names&gt;</span><span class="plain-syntax">, </span><span class="identifier-syntax">EQUALITY_RELATION_NAME</span><span class="plain-syntax">));</span>
<span class="plain-syntax">        </span><a href="3-bp.html#SP8" class="function-link"><span class="function-syntax">BinaryPredicates::set_index_details</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">R_equality</span><span class="plain-syntax">, </span><span class="string-syntax">"value"</span><span class="plain-syntax">, </span><span class="string-syntax">"value"</span><span class="plain-syntax">);</span>
<span class="plain-syntax">    }</span>
<span class="plain-syntax">}</span>

<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Calculus::Equality::stock_spatial</span><button class="popup" onclick="togglePopup('usagePopup3')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup3">Usage of <span class="code-font"><span class="function-syntax">Calculus::Equality::stock_spatial</span></span>:<br/><a href="3-ter.html#SP2">&#167;2</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">bp_family</span><span class="plain-syntax"> *</span><span class="identifier-syntax">self</span><span class="plain-syntax">, </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">n</span><span class="plain-syntax">) {</span>
<span class="plain-syntax">    </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">n</span><span class="plain-syntax"> == </span><span class="constant-syntax">1</span><span class="plain-syntax">) {</span>
<span class="plain-syntax">        </span><span class="identifier-syntax">a_has_b_predicate</span><span class="plain-syntax"> =</span>
<span class="plain-syntax">            </span><a href="3-bp.html#SP10" class="function-link"><span class="function-syntax">BinaryPredicates::make_pair</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">spatial_bp_family</span><span class="plain-syntax">,</span>
<span class="plain-syntax">                </span><a href="3-bptd.html#SP3" class="function-link"><span class="function-syntax">BPTerms::new_full</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><span class="identifier-syntax">EMPTY_WORDING</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">),</span>
<span class="plain-syntax">                </span><a href="3-bptd.html#SP2" class="function-link"><span class="function-syntax">BPTerms::new</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">NULL</span><span class="plain-syntax">),</span>
<span class="plain-syntax">                </span><span class="identifier-syntax">I</span><span class="string-syntax">"has"</span><span class="plain-syntax">, </span><span class="identifier-syntax">I</span><span class="string-syntax">"is-had-by"</span><span class="plain-syntax">,</span>
<span class="plain-syntax">                </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">,</span>
<span class="plain-syntax">                </span><span class="identifier-syntax">PreformUtilities::wording</span><span class="plain-syntax">(</span><span class="function-syntax">&lt;relation-names&gt;</span><span class="plain-syntax">, </span><span class="identifier-syntax">POSSESSION_RELATION_NAME</span><span class="plain-syntax">));</span>
<span class="plain-syntax">    }</span>
<span class="plain-syntax">}</span>

<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Calculus::Equality::stock_empty</span><button class="popup" onclick="togglePopup('usagePopup4')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup4">Usage of <span class="code-font"><span class="function-syntax">Calculus::Equality::stock_empty</span></span>:<br/><a href="3-ter.html#SP2">&#167;2</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">bp_family</span><span class="plain-syntax"> *</span><span class="identifier-syntax">self</span><span class="plain-syntax">, </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">n</span><span class="plain-syntax">) {</span>
<span class="plain-syntax">    </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">n</span><span class="plain-syntax"> == </span><span class="constant-syntax">1</span><span class="plain-syntax">) {</span>
<span class="plain-syntax">        </span><span class="identifier-syntax">R_empty</span><span class="plain-syntax"> = </span><a href="3-bp.html#SP9" class="function-link"><span class="function-syntax">BinaryPredicates::make_equality</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">empty_bp_family</span><span class="plain-syntax">,</span>
<span class="plain-syntax">            </span><span class="identifier-syntax">PreformUtilities::wording</span><span class="plain-syntax">(</span><span class="function-syntax">&lt;relation-names&gt;</span><span class="plain-syntax">, </span><span class="identifier-syntax">EMPTY_RELATION_NAME</span><span class="plain-syntax">));</span>
<span class="plain-syntax">        </span><a href="3-bp.html#SP8" class="function-link"><span class="function-syntax">BinaryPredicates::set_index_details</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">R_equality</span><span class="plain-syntax">, </span><span class="string-syntax">"value"</span><span class="plain-syntax">, </span><span class="string-syntax">"value"</span><span class="plain-syntax">);</span>
<span class="plain-syntax">    }</span>
<span class="plain-syntax">}</span>
</pre>
<p class="commentary firstcommentary"><a id="SP4" class="paragraph-anchor"></a><b>&#167;4. Problem message text.</b></p>

<pre class="displayed-code all-displayed-code code-font">
<span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="function-syntax">Calculus::Equality::describe_for_problems</span><button class="popup" onclick="togglePopup('usagePopup5')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup5">Usage of <span class="code-font"><span class="function-syntax">Calculus::Equality::describe_for_problems</span></span>:<br/><a href="3-ter.html#SP2">&#167;2</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">bp_family</span><span class="plain-syntax"> *</span><span class="identifier-syntax">self</span><span class="plain-syntax">, </span><span class="identifier-syntax">OUTPUT_STREAM</span><span class="plain-syntax">,</span>
<span class="plain-syntax">    </span><span class="reserved-syntax">binary_predicate</span><span class="plain-syntax"> *</span><span class="identifier-syntax">bp</span><span class="plain-syntax">) {</span>
<span class="plain-syntax">    </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">;</span>
<span class="plain-syntax">}</span>
<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Calculus::Equality::describe_for_index</span><button class="popup" onclick="togglePopup('usagePopup6')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup6">Usage of <span class="code-font"><span class="function-syntax">Calculus::Equality::describe_for_index</span></span>:<br/><a href="3-ter.html#SP2">&#167;2</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">bp_family</span><span class="plain-syntax"> *</span><span class="identifier-syntax">self</span><span class="plain-syntax">, </span><span class="identifier-syntax">OUTPUT_STREAM</span><span class="plain-syntax">,</span>
<span class="plain-syntax">    </span><span class="reserved-syntax">binary_predicate</span><span class="plain-syntax"> *</span><span class="identifier-syntax">bp</span><span class="plain-syntax">) {</span>
<span class="plain-syntax">    </span><span class="identifier-syntax">WRITE</span><span class="plain-syntax">(</span><span class="string-syntax">"equality"</span><span class="plain-syntax">);</span>
<span class="plain-syntax">}</span>
<span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="function-syntax">Calculus::Equality::describe_empty_for_problems</span><button class="popup" onclick="togglePopup('usagePopup7')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup7">Usage of <span class="code-font"><span class="function-syntax">Calculus::Equality::describe_empty_for_problems</span></span>:<br/><a href="3-ter.html#SP2">&#167;2</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">bp_family</span><span class="plain-syntax"> *</span><span class="identifier-syntax">self</span><span class="plain-syntax">, </span><span class="identifier-syntax">OUTPUT_STREAM</span><span class="plain-syntax">,</span>
<span class="plain-syntax">    </span><span class="reserved-syntax">binary_predicate</span><span class="plain-syntax"> *</span><span class="identifier-syntax">bp</span><span class="plain-syntax">) {</span>
<span class="plain-syntax">    </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">;</span>
<span class="plain-syntax">}</span>
<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Calculus::Equality::describe_empty_for_index</span><button class="popup" onclick="togglePopup('usagePopup8')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup8">Usage of <span class="code-font"><span class="function-syntax">Calculus::Equality::describe_empty_for_index</span></span>:<br/><a href="3-ter.html#SP2">&#167;2</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">bp_family</span><span class="plain-syntax"> *</span><span class="identifier-syntax">self</span><span class="plain-syntax">, </span><span class="identifier-syntax">OUTPUT_STREAM</span><span class="plain-syntax">,</span>
<span class="plain-syntax">    </span><span class="reserved-syntax">binary_predicate</span><span class="plain-syntax"> *</span><span class="identifier-syntax">bp</span><span class="plain-syntax">) {</span>
<span class="plain-syntax">    </span><span class="identifier-syntax">WRITE</span><span class="plain-syntax">(</span><span class="string-syntax">"never-holding"</span><span class="plain-syntax">);</span>
<span class="plain-syntax">}</span>
</pre>
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